Geometric quantization on presymplectic manifolds
- Cite this article as:
- Vaisman, I. Monatshefte für Mathematik (1983) 96: 293. doi:10.1007/BF01471212
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In this paper, we discuss the possibilities of adapting geometric quantization to presymplectic manifolds, i.e., differentiable manifoldsM2n+k (k>0) endowed with a closed 2-form ω of rank2n. We show that such an adaptation is possible in various manners, and that, as a general idea, it reduces the quantization onM to quantization on the symplectic quotientM/V, whereV is the foliation defined by the annihilator of ω.